For zebrafish skin and other biological patterns, continuum models have the benefit of being analytically tractable, and they provide a broad perspective on the overarching features (such as density-dependent motion [1]}, [2]} or short-range activation and long-range inhibition [3]}, [4]})
that may be at work. On the other hand, agent-based and cellular automaton modelsResearchers use the terms “agent-based", “individual-based", and “cellular automaton" to describe a rich diversity of models. In this manuscript, “agent-based" means a model that works at the scale of agents—e.g., cells—interacting in continuous space. We distinguish this from what we call “cellular automaton" models, which also focus on the dynamics of agents, but in which space is discrete; see Figure REF ., not analytically tractable using traditional techniques, are often closer to the underlying biology and can make detailed predictions about cell interactions. Uncovering how different types of models are related is a rich mathematical problem, and, because it breaks down silos and allows us to bring the predictions of different studies together, it has important biological applications. To this end, much work has focused on relating macroscopic and microscopic approaches. In the case of zebrafish patterns, for example, Bullara et al. [5]}, Konow et al. [6]}, and Volkening et al. [7]}, [8]} developed continuum models for cell density alongside microscopic models. While open questions certainly remain in relating macroscopic and microscopic models, much less work has focused on understanding the relationship between different microscopic models, such as on-lattice and off-lattice approaches. We highlight the studies of Osborne et al. [9]} and Plank et al. [10]} on cell behavior as examples.
